[ENCH 403] - Final Exam Guide - Ultimate 67 pages long Study Guide!

• School: University of Calgary
• Department: Chemical Engineering
• Course: ENCH 403
• Professor: Sundararaj

Document Summary

For 2-dimensional steady-state conduction, the general conduction equation simplifies to: (cid:2870)(cid:1846)(cid:1876)(cid:2870)+(cid:2870)(cid:1846)(cid:1877)(cid:2870)=(cid:882) There are 3 methods of solving this: analytical: separation of variables, graphical: shape factor, numerical: finite difference. Generally time-consuming and not possible in many cases: transform variable to get homogeneous boundary conditions: (cid:4666)(cid:1876),(cid:1877)(cid:4667)=(cid:1846)(cid:4666)(cid:1876),(cid:1872)(cid:4667) (cid:1846) (cid:2870)(cid:1876)(cid:2870)+(cid:2870)(cid:1877)(cid:2870)=(cid:882) (cid:4666)(cid:882),(cid:1877)(cid:4667)=(cid:4666),(cid:1877)(cid:4667)=(cid:882) (cid:4666)(cid:1876),(cid:882)(cid:4667)=(cid:882) (cid:4666)(cid:1876),(cid:4667)=(cid:883) (cid:4666)(cid:1876),(cid:1877)(cid:4667)=(cid:1850)(cid:4666)(cid:1876)(cid:4667) (cid:1851)(cid:4666)(cid:1877)(cid:4667, solve separately to get: (cid:1856)(cid:2870)(cid:1850)(cid:1856)(cid:1876)(cid:2870)+(cid:2870)(cid:1850)=(cid:882) (cid:1856)(cid:2870)(cid:1851)(cid:1856)(cid:1877)(cid:2870)+(cid:2870)(cid:1851)=(cid:882, general solutions: (cid:1850)=(cid:2869)(cid:1855)(cid:1867)(cid:1871)(cid:1876)+(cid:2870)(cid:1871)(cid:1866)(cid:1876) (cid:1851)=(cid:2871)(cid:1857) +(cid:2872)(cid:1857, general form: =(cid:4666)(cid:2869)(cid:1855)(cid:1867)(cid:1871)(cid:1876)+(cid:2870)(cid:1871)(cid:1866)(cid:1876)(cid:4667)(cid:4666)(cid:2871)(cid:1857) +(cid:2872)(cid:1857)(cid:4667) For infinite medium cases, characteristic length is: (cid:3030) (cid:4672)(cid:2872)(cid:4673)(cid:2869)/(cid:2870: where (cid:3046)= surface area (cid:3030) (cid:3046)(cid:3046) = (cid:3046)(cid:4666)(cid:1846)(cid:2869) (cid:1846)(cid:2870)(cid:4667) See table 4. 1 for various s and qss of different configurations. Conduction heat transfer rates from object to infinite medium can be reported as dimensionless conduction heat rate: Numerical method determines temperature at discrete points. Reference points assigned to center of each region is a node. See table 4. 2 for nodal finite-difference equations. Transient problems typically arise when boundary conditions of a system are changed: removing a kettle from a heated stove.